An article published in Geography (July 1980) used multiple regression to predict annual rainfall levels in California. Data on the average annual precipitation (y), altitude (x1), latitude (x2), and distance from the Pacific coast (x3) for 30 meteorological stations scattered throughout California are saved in the CALIRAIN file. (Selected observations are listed in the table above.) Consider the first-order model

y = β0 + β1x1 + β2x2 + β3x3 + ε.

a. Fit the model to the data and give the least squares prediction equation.

b. Is there evidence that the model is useful in predicting annual precipitation y? Test, using α = .05.

c. Find a 95% prediction interval for y for the Giant Forest meteorological station (station 9). Interpret the interval.

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Avg. Annual Precipitation y (inches) 2 Latitude x 2 (degrees) Distance from Coast x3 (miles) Altitude 0 Station X1 (fee 1. Eureka 2. Red Bluff 3. Thermal 4. Fort Bragg 5. Soda Springs 39.57 23.27 18.20 37.48 49.26 43 341 4152 40.8 40.2 33.8 39.4 39.3 97 70 6752 150 9.94 4.25 1.66 74.87 15.95 32.7 34.1 36.5 41.7 39.2 26. San Diego 27. Daggett 19 2105 一178 35 85 194 28. Death Valley 29. Crescent City 30. Colusa 91